NASA Technical Memorandu_..]_0_.!_67- . _ i ...................................

AIAA-90-2417 _ ii_ _......................... _ 15 " - i_:=

A Modeling TeChnique for STOVL

-:'_== Eject0rand-VoiumeDynamics -

C.K. Drummond and W_S. B0ra_iewicz

Lewis Research Center

Cleveland, Ohio ....

(NASA-TM-I03167) A MOD[LING TECHNIOUE FOP, Ng0-2P569 :_:_:

$TUVL EJECTOR A_O VOLUM_ DYNAMICS (NASA)

Uncl _s

G3/07 02615R8

prepared for the _- ................

26th Joint Propulsion conference

cosponsored by the AIAA, SAE, ASME, and ASEE

- Orlando, Florida, July 16-18, 1990

A MODELING TECHNIQUE FOR STOVL EJECTOR AND VOLUME DYNAMICS

C. K. Drummond* and W. s. Barankmwacz

National Aeronautics and Space Administration

Lewis Research Center

Cleveland, Ohio 44135

05

t-v-)

I

I..ul

&b.ar_ara

New models for thrust augmenting ejector performance

prediction and feeder duct dynamic analysis are presented

and applied to a proposed STOVL aircraft configuration.

Central to the analysis is the nontraditional treatment of

the time-dependent volume integrals in the otherwise

conventional control-volume approach. In the case of the

thrust augmenting ejector, the analysis required a new

relationship for transfer of kinetic energy from the primary

flow to the secondary flow. Extraction of the required

empirical corrections from current steady-state experimental data is discussed; a possible approach for modelling

insight through CFD is presented.

Nomenclature

A cross-sectional area

to jet half-width

B channel half-width

C L empirical coefficient

d effective nozzle diameter

It enthalpy

KE kinetic energy

m mass flowrale

m,o control volume mass

A:t momentum flux

M co control volume momentum

A,ILe Mach number of primary nozzle flow

P pressure

t time

v vclocity

[r volume

h/ unit depth of control volume

x transverse coordinate

z strcamwise coordinate

p density

+ self-similar profilc flmction

o lurbulcnt flow constanl

_, dimcnsionlcss transvcrsc coordinate

_ab_crJ_t_

cv control volume

e entrained stream

m primary stream centerline

1s secondary steam at station 1

1 p primary stream at station 1

*Aerospace Engineer, Member AIAA

**Aerospace Engineer

Copyright © 1990 by the American Institute of Aeronautics

and Astronautics, Inc. No copyright is asserted in the

United States under Title 17, U.S. Code. The U.S. Government has a royalty-free license to exercise all rights under

the copyright claimed herein for Governmental purposes.

All other rights are reserved by the copyright owner.

Thrust augmenting ejectors are candidate componenets

for powered lift propulsion subsystems of Short Take-Off

Vertical Landing (STOVL) aircraft. Figure 1 illustrates that

a typical ejector is a mechanically simple device in which a

convergent nozzle is placed within a shroud; in the case of

STOVL aircraft, the wing and fuselage act as part of the

shroud. Except for a valve to control flow through the nozzle

feeder duct, no other parts of this system are required to

move during ejector operation (portions of the ejector can,

however, fold away for forward flight).

Interest in the dynamic responsc of an ejector system

extends from an effort to develop a complete propulsion

system simulation for ASTOVL aircraft (Mihalocw and

Drummond, 1989; Akhtcr et. al., 1989). Propulsion system

simulations that run in real-time are an important part of

research on design mcthodologies for Integrated Flight and

Propulsion Control (IFPC) systems. In this context a useful

ejector characteristic to know is the frequency response of

ejector thrust output (due to a change in the primary nozzle

flow condition). If the ejector response is outside the

bandwidth of the flight control system (see Figure 2) then

a simple quasi-steady ejector model is all that is needed for

the propulsion system simulation. In such a case the ejector

model could be, for instance, a simple table look-up; this

approach readily meets real-time simulation constraints

(on the AD100 real-time simulation computer, a table

look-up consumes about 2 microseconds).

On the other hand, if the ejector response falls within

the range of the flight control (or if a new ejector system

has an unknown response) a high-fidelity ejector model

must be constructed. Since accuracy is typically synonymous

with a significant amount of model detail, constructing a

transient ejector model to mcet the real-time simulation

requirement is a fairly difficult task. Also, the need to

predict transient ejector performance aggravatcs a more

fundamental modelling problem extending from an

incomplete picture of steady-state ejector phenomena.

For simplicity in discussion and analysis, an ejector

system is usually subdivided along functional lines intoan

inlet, mixing region, and diffuser. Porter and Squires (1981)

present a perspective whereby an ejector gas flow undergoes changes analogous to those of a gas turbine: both

systems have an inlet and nozzle (diffuser), but in an ejector

the compression, combustion (energy addition), and turbine processes are contained within the mixing region.

Compression of and energy addition to the secondary flow

results from interaction with the primary flow; the energy
obtainedbyexpansionof the primary nozzle flow is analogous to the energy input a turbine provides. It is interesting

that the potential for augmentation of the primary ejector

thrust is understood clearly to be a function of the reduced

"ambient" pressure the primary nozzle discharge sees; what

is less understood is the detailed mechanism of the

primary-secondary entrainment phenomenon responsible

for that environment. Central to improving our understanding of the interaction between the primary and secondary flow is a better understanding of the physics behind

turbulent, compressible flow shear layers (Goebel and

Dutton, 1990, provide a recent look at this problem).

One approach to the ejector analysis is based on first

principles and typically blends the mean value equations for

momentum, energy and heat with phenomenologial models

of turbulence for closure (Anderson et. al., 1984; Townsend,

1980). Finite-difference, finite-element, or spectral methods of analysis are then employed for the discretization and

solution of the final system of equations (Peyret and Taylor,

1983). These solution methods are representative of

modern Computational Fluid Dynamics (CFD). Although

CFD provides a rigorous approach to analysis of the

flowfield, it is not expected that real-time solutions are

achievable in the forseeable future.

Another problem concerns identification of the

appropriate boundary conditions and turbulence model to

use for the description of the mixing region. It appears the

state-of-the-art provides steady-flow predictions more

accurate in an integral sense (pressure, thrust) than

pointwise (velocity). For instance, Deese and Agarwal

(1988) investigated several CFD analyses (including their

own) and remark on the general failure to produce "acceptable" velocity profiles. The capability to predicit thrust

is encouraging, but wall shear stress estimates will not be

more accurate than the velocities computed. Modern CFD

analyses designed to attack these problems is an active area

of research (see, for instance, Lowrie, 1990; Choi and Soh,

1990).

Control-Volume Approach

An alternative to CFD is the control-volume approach.

In this case the governing equations express "bulk" conservation of mass, momentum, and energy. Although the

control-volume method greatly simplifies the mathematical

analysis, the opportunity to introduce a detailed mathematical description of any transport mechanisms is often

lost. Real-flow effects are generally introduced through loss

factors (nozzle coefficient; wall friction factor) or specified

skewness conditions (non-uniform secondary or mixed flow

profiles). By default, such corrections are accurate for the

model tested, but tend to be configuration dependent and

have unknown scale effects. Despite criticizm that

control-volume predictions devoid of empirical correction

factors do not rigourously account for mixing, entrainment,

and boundary-layer effects, this approach has been the

foundation for many steady-flow ejector performance

predictions exhibiting rapid execution speed of execution

and acceptable engineering accuracy. We find this to be an

attractive foundation for the exploration of a transient flow

simulation.

Here, a transient flow is a 'temporary' unsteady flow,

associated with, for example, a change in ejector operation

from one steady-state condition to another. Contrast this

with oscillatory flows in which a periodic time-asymptotic

flow character is exhibited. Ejectors utilizing pulsed primary nozzle flows are of the latter type. In the present

simulation the focus on transient, not oscillatory, ejector

phenomena descends from flight-critical aircraft fight

control scenarios; an example would be transition to forward flight from vertical take-off.

A basic difficulty in application of the control-volume

method to the study of transient flows is in the treatment

of the time-dependent volume integrals -- unless you

consider the flow quasi-steady, it is essential these terms be

included in the problem formulation. One solution to this

modelling problem to draw in as many assumed features of

the flowfield as possible.

Scope of Work

An empirically based model for the jet mixing turbulent

interaction region is explored within the framework of a

control volume analysis. Three fundamental assumptions

are discussed in the present work that reduce the transient

ejector analysis problem to an attractively simple system of

equations. We also remark on a control-volume approach

to simulation of duct dynamics. In comparison with the

ejector analysis, the mathematical treatment is considerably

simplified by the absence of a secondary flow. Generally

the focus of discussion is on the transient features of the

analysis since the treatment of steady-state flows is given

in, for instance, Addy and Dutton (1974).

Estimation of the empirical coefficients required in the

control-volume method of analysis is discussed. Typical

results from the ejector and duct analysis for a proposed

STOVL aircraft are presented. Preliminary finite-element

CFD results for the ejector mixing region are also presented; CFD is being pursued as one means to augment the

ejector modeling process.

In an unsteady flow problem, considerable mathematical convenience follows when a quasi-steady flowfield

response can be assumed -- the time-derivative terms in the

governing differential equations can be dropped. At each

instant in time the flow is assumed to respond instantly to

boundary condition changes. The validity of such an

assumption, however, requires the characteristic time of the

forcing function to be the same as (or greater than) the

relaxation time of the flow. For a given flowfield disturbance, pressure forces respond more quickly than viscous

forces, so the former are therefore more appropriately

treated as quasi-steady.
Notethatthemixingregionshearlayerphysicsarethe

cause of a situation that yields pressure gradient effects in

the inlet and diffuser. It is therefore reasonable to assume

the inlet and diffuser behave in a quasi-steady fashion. In

the present work the analysis focuses on describing the

mixing region characteristics shown in Figure 3.

The development begins with some comments on the

mass, momentum, and energy balances for a mixing region

control volume. Then, the application of serf-similar

velocity profiles to the governing equations is presented. In

the last section we discuss division of the energy balance

into the (usual) thermal energy balance and a new function

for mechanical energy.

_matr_-Y_olttme_Equ atiom

Several assumptions simplify the mixing region mathematical representation without unduly compromising the

physics of interest. A one-dimensional flow assumption

limits field variable gradients to occur along (but not across)

the streamwise axis. Viscous, blockage, and Reynolds

number effects are neglected. Gases are assumed thermodynamically perfect (constant specific heat) and

described by the equation of state. The primary and

secondary flows can be of different total pressure and

temperature, but equality of static pressure at the point of

confluence of the two jets is enforced. These assumptions

are applied to the following integral form of the conservation equations (see Thompson, 1972):

d dtrne° f _ pv" ndA (1)

_tfvPVdV=-SApv(v.n)dA-fan.(pl)dA (2)

O h+--- dV=- p h+__ v'ndA

2

(3)

Equation (3) represents the energy equation derived from

the first law of thermodynamics -- this form of the energy

balance is known as the general energy equation. Since

discontinuities in, for instance, entropy, are not included in

this formulation, the present formulation will not effectively

describe shock flows. The general energy equation is a

balance of energy due to heat and work. The product of the

local fluid velocity and the momentum equation (Eqn.2)

yields the mechanical energy equation. Subtracting the

mechanical energy equation from the general energy

equation produces the heat equation, the latter of which is

a simple statement of conservation of heat content in the

ejector mixing region,

p(h- )dv = - f ph,,. ndA (4)

In the present work, Eqn.(4) is retained to represent the

heat balance, and (as discussed later) a semi-empirical

kinetic energy exchange model is substituted for the

mechanical energy counterpart.

Some important features of the mixing region flowfield

are shown in Figure 3. Primary and secondary potentialcore regions are characterized by a uniform axial velocity

(and no transverse component). The inside and outside

bounds of the jet shear layer are defined by conditions of,

respectively, the primary and secondary potential flows.

Momentum transfer from the primary jet results in the

eventual consumption of the primary core. Generally the

flowfield is considered in a "developing" state prior to the

point at which the wall boundary layer meets the outer jet

boundary.

_App.toximat_

Extensive experimental data supports the Abramovich(1963) non-dimensional velocity representations of 2-D

planar co-flowing free jets:

v = v.(l-¢)+v..4_ = /(¢) (5)

where

and

,i,(_) __ ((1-_s)2.0<-_<-I 1

o, i_<__<_

(6)

= x/b, _ = _/b (7)

Inclusion of the core region requires a slight modification

of these profiles; deta!l s are given in Abramovich(1963).

In comparison with the Ablramovich free jet approximation, ejectors involve a confined jet in which a streamwise

pressure gradient exists. An issue to therefore be resolved

is the accuracy to which the Abramovich profiles represent

the ejector flow. As a practical matter these self-similar

profiles have been used extensively with acceptable accuracy in fluidized bed gas cleaning applications (Donsi et.

al., 1980; Tan, 1982). Although the pressure gradient is in

the opposite direction (than that of the ejector), the

gradients are significant (up to 100%); this situation

encourages the application of Abramovich's profiles outside of his original set of assumptions. A more thorough

examination of this approximation appears to be possible

if, for instance, raw data from Storms(1989) LDV work or

McLachlan et. al. (1984) were curve-fit accordingly.

Since there is a static pressure matching condition at

the jet boundary, a uniform transverse pressure distribution

is assumed; in the longitudinal (axial) direction a finite

pressure gradient exists (Again, this feature partially distinguishes free-jet and confined-jet analyses). This reduces

the general pressure profile to the form

p-/:),

= A(_)= l (8)

p.,- p.

To avoid complexity in the use of the ideal gas law, density

also has a uniform profile. Since this implies a uniform

temperature profile, a compromise has been introduced in

the mixing region representation for temperature (Abramovitch suggests the non-dimensional temperature profile

be approximated by the square root of the velocity profile).
Application to the Conservation Equations

Figure 4 illustrates the finite volume descretization

employed in the present work. Since the implicit assumption

is that the self-similar profiles are the link between the flow

streams in the transverse direction, descretlzation only

occurs in the streamwise direction. To capture a representative variation in flowfield characteristics (Figure 3) it

is necessary to divide the mixing region into at least 3

elements. We generalize the analysis by defining a generic

element, k, bounded by surfaces at i andj.

Consider the application of the self-similar profiles to

the mass conservation equation. Based on our previous flow

assumptions, Equation (1) simplifies to the form

(dra) = m, - rhi (9)

where the mass flux is now written

ria, = p,c,dd = 21V p,u,d_ (10)

From which integration over the self-similar profiles yields

m, = 21gb,p,(O.45v,_+O.fSv_+(_-l)v_),

= 21db,Z I (11)

The time-derivative term in the mass conservation equation

is given by

"_ k = 2IJBAz (12)

/

where the characteristic density for the finite volume is now

approximated by the value of the density at station ] (in

practice this is a good assumption as long as field variable

gradients are "modest" in size). If the characteristic jet

expansion width, b, also assumes its value at j, then

substitution and re-arrangement of the continuity equation

yields

(do) = b,Z,., - b,Z,., (13) 7-ff j BAz

Computation of the jet half-width, b, derives from the

momentum equation for incompressible flow, applied to

thefirst finite volume; a rectilinear jet expansion is assumed

therefrom and compressible flow restored for subsequent

calculations (In light of thc recent work of Goebel and

Dutton (1990), this procedure for computing the jet

expansion angle may need to be refined).

When the self-similar profiles are substituted into the

momentum balance, equation (2), the jet centerline velocity

derivative can be shown to be

dt Jj 2[gbjLkz p _- *

where

_- 0.45

Fl 0.45

M k = 2Wb,(Z2,,+_P,)

(15)

-2Wb,(Z2. j + _Pj) (1 6)

f t z

Zz = Jo P_Ukd_ (17)

Note in equation (14) that the centerline velocity derivative

is a function of the density derivative, equation (13).

Introduction of an ideal gas assumption simplifies the

heat equation to the form

-_ pdV = - pyv. ndA (18)

Non-dimensional velocity and pressure profiles provide the

pressure derivative result

(d_t) bkZ,+bk.,Z, bkZo-bk,,Zo =_ +(v-i) (19)

k AzB AzB

where Z 1 has been derived previously and Z 0 is given at

each station by

Zo,, = f]p,Ad_ (20)

Equations (13), (14), and (19) are the three differential

equations required for computing the time derivatives of

gas density, pressure, and jet centerline velocity in the

ejector mixing region. Closure for the problem requircs

definition of the entrained flow state.

Entrained Kinetic Enerffy_

Analysis of the primary and secondary flow interaction

has not, to this point, been completed. By themselves, the

self-similar profiles close the loop for steady-stateflows, but

not transient ones. This section provides an approximation

for the turbulent flow kinetic energy exchange mechanism

to characterize the influence of primary flow changes on

the secondary flow. Knowledge of the total changc in

secondary flow kinetic energy permits updates to the

secondary flow state during integration of the field variable

time derivatives.

= =

Computations for a specified steady-state condition

show that the change in kinetic energy due to mLring is not

the same for the Secbndary fl0W as it is for the primary. In

fact, the gain in kinetic energy of the secondary flow is

entirely due to the mixing process, while the mixing loss of

the primary flowis only a fraction of its total loss. In balance,

the total change of kinetic energy of the primary flow is

greater than that of the secondary flow.

In the works of Chow and Addy(1964) and Korst and

Chow(1966) the relationship betwecn the change in

entrained flow kinetic energy and the total primary flow

kinetic energy for a shear layer are discussed, and the results

can be expressed in the functional form:

AKE,s = F(KE,,. O} (21)
whereit wasempiricallydeterminedthat

- 12(1+0.23M_e) (22)

Thedifficultywiththekineticenergyfunctionasgivenabove

isthatit representsaquasi-steadyconstant-pressure flow

approximation and therefore cannot be used in its present

form for the transient flow analysis. To entertain local

transport of energy, consider the change in secondary flow

to be a combination of changes in primary and secondary

flow kinetic energies due to mixing alone,

where the subscript m denotes the change in kinetic energy

due exclusively to mixing. Numerical experiments suggest

the form

_xKE','y - eXKE''_'l,._+_xK_',, _C, (24)

This engineering approximation results in the introduction

of an undetermined constant, C ,. In the present work the

value of the constant is determined by matching transient

solution asymptotes with steady-state performance data (an

example is presented later).

Computation of the gain in secondary flow kinetic

energy due to mixing is given by

_KE lS,r¢_ = 'f.)o 5-2 )d_ (2S)

where gdefines the jet boundary streamline (for which the

primary mass flow through station i is equal to primary mass

flow through j). For the present discussion this dividing

streamline position is assumed known; Korst and

Chow(1966) discuss the typical approach of analysis.

Expanding the equation for the change in kinetic energy

yields

AKEIs._=WbO (va-vv2,)d_+ (va-vo_,)d_;

(26)

Substitution of the self-similar profiles into this expression

and integrating the result provides

AKEls.._ =NWbp(va(Hl + H s - F a - F4)

+v._v2_(Ha-F,)+o_v.Hz+V_H4} (27)

where the detailed expressions for the integrals H i and Fi

are given by Drummond(1988). It should be noted that in

the present work the integrals are independent of time.

Similar to the way in which the change in secondary flow

kinetic energywas computed, the energy loss of the primary

flow is given by

AKEi,., = Jo pv_-_ -_

(28)

where the limits of integration reflect interest in the domain

of the primary jet cross-section.

Evaluation of the integral at station i yields the result

AKE ,e,,. = I'/bp(vaH, + v.v_H2 + v_v_Ha + v_H4

-v_F,-v.v_Fa) (29)

The expressions for the integrals implied in Fi and H i can

be obtained from Drummond(19gg).

It is recognized that the mixing length theory of Korst

has only been verified for steady-state flow and, furthermore, that a constant pressure assumption was made in his

analysis. For the transient ejector work, Korst's theory is

simply employed as a springboard for a new functional

relation between the primary and secondary flows.

Although the detailed form of the function has not been

validated, one must admit that the basic model provides a

rational foundation for energy exchange and does allow

flexibility in future modelling efforts.

_Sammar_

Density, velocity, and temperature are the unknown

ejector mixing region field variables. The proposed control

volume analysis asks the sub-region be characterized by an

'entrained flow' node and a 'jet centerline' node. The initial

value problem links the two nodes through a form of the

integral equations where a self-similar profile assumption

has been blended in. To proceed forward in time, then, (a)

integrate the three jet centerline equations forward one

time step, Co) compute the entrained velocity from the

kinetic energy exchange approximation, and (c) update the

entrained flow density and pressure by assuming equilibrium with the primary flow.

Iala2alal.w_

Feeder ducts and tailpipes are 'large-volume' STOVL

propulsion system components whose dynamic response

(so called, volume dynamics) are of interest when (a)

coupling of static sub-system components is necessary, or

(b) gas dynamics effects are potentially significant. A model

that satisfies both of these situations is desired for the

general ejector system simulation objective.

The proposed model follows directly from the governing

equations for mass, momentum, and energy given by

Eqns.(1)-(3). All of the simplifying assumptions stated for

the ejector are also assumed here.

As before, mass conservation takes the form of a density

derivative

(dp) _- k = m,-mVk I = rh,-ria AAx 1 (30)

where an overbar indicates a volume-average quantity.

5
Flow momentumchangesin ductsare generally

attributableto variationsin cross-sectional areaor the

frictionassociatedwithrealflows;thegoverningdifferential

equationisavectorexpression, butundertheassumtion

theunitnormalspointoutwardfromeachboundarythere

resultsthescalarbalance

d

d---_(pvV)k = M,-Mj+t e (31)

where the scalar form of the momentum is

M = vrh + PA

In this work an idealized expression for the internal

resistance of the duct shown is given by

i A,) (32) f" = -PdA _" -_(P,+P,)(A,-

where the absence of frictional effects should be noted.

Carrying through the differenfiotion in time and rearranging results in the following equation

(dr) 1 vdp dt _ _Ax(M,-M,+?)-._d---[ (33)

The characteristic velocity v is a weighted average of the

inlet and exit control volume velocities

v = _v,+ (1 -_)v, (34)

where _ is a weighting parameter ranging in value from 0

to 1.

In the duct analysis the general power equation is used

since it includes representations of thermal and kinetic

energy,

p h+w-c-jj, = E,-E, (3S)

where

The time-dependent term can be rearranged to read

clot p h + -_ - -ff , y 1 d t d---[+ 2 dr),

and from this an expression for the pressure derivative

obtained

1 (8/9) F "-[--clc vZdP} (37) y- 1 "_ k= {c0'- ') \pv_-+Td-_- ,

Equations (30), (33), and (37) are the required differential

equations to integrate for the prediction of duct dynamics.

Results

A step-change forcing function is a simple yet effective

transient for examining dynamic system response. In this

work a step-change in primary nozzle flowrate is imagined

to be a 'worst-case' scenario for STOVL ejector operation

and is therefore considered an appropriate test for the

simulation. For demonstration purposes a flowrate stepchange from 18.7 to 21.9 lbm/sec is chosen because (a)

experimental steady-state data at each of these operating

points is available, and ,!b) the 17% change in primary

flowrate is well beyond a small"-perturbation examination

(this exercises the system non-linearities). The rectangular

mixing region of the proposed STOVL ejector is approximately 1 ft wide (at the throat), 9 ft in depth (along the wing

chord axis), and 0.9 ft long. A 260OF primary flow is used

to entrain air at ambient conditions. A hover condition is

assumed (no forward ejector velocity). The feeder duct was

assumed to be straight, 15 ft long, and have a constant 1.1

ft diameter.

F,jcclomPredictions

With the STOVL mixing region subdivided into five

finite-volumes (along the flow axis), the individual

control-volume length of 0.18 ft combined with a characteristic mixing region velocity of, say, 500 ft/s yields a

residence time (elapsed time for the primary nozzle flow

to reach the diffuser exit plane) for the flow of approximately 0.4 ms. The numerical time step must be less than

this value. A estimate of the stability limit value A t = .12ms

is given by the Courant approximation (At < O.SAx/u).

To avoid infringing on this stability limit a computational

time step of 0.1 ms was chosen for the present work. An

explicit time stepping scheme is appropriate for this

application since the optimal weighting factors for an

implicit approach are generally a function of time.

The empirical coefficient C 1 in the transient analysis is

required for calibration of the function for primary-to--

secondary kinetic energy exchange, Equation 24. For a

step-function change in the primary flowrate, the ejector,

initially operating at a steady-state condition, asymptotically

approaches a second steady-state. The desired C I value is

the one that provides a match between the predicted

asymptote and the known thrust at the second state. Thrust

predictions are shown in Figure 5; the "best" C1 value

appears to be between 0.3 and 0.35.

For a 760 ft/s initial primary flow velocity, it appears

the 1,2ms flow residence time is slightly less than half the

3 millisecond interval for the thrust to reach a new maximum, Oscillations in thrust after that point appear to settle

in about 5 milliseconds. This profile suggests a second-order

frequency response of the ejector. Under a second-order

assumption the ejector test case suggests a 0.75 ejector

damping ratio and a natural frequency on the order of

300Hz.

An (initially) unexpected feature of the thrust profile is

the dip in thrust immediately following the step-change in

primary nozzle efflux. Examination of the field variable

profiles reveals this is not a numerical problem, but that the

increase in static pressure associated with the instantaneous

change in driving flow temporarily reduces the favorable

sub-ambient pressure environment (required for a potential in thrust augmentation) at the primary nozzle discharge.

After a short period, the shear layer energy transfer
becomescommensurate withtheincr.easeinprimaryflow

energyto overcomethiseffect,andtheresponsethen

continuesinanintuitivelyexpectedmanner.

Transientflowcalculationsfortheejectorfeederduct

werebasedontheflowprofilepreviouslydescribedforthe

ejectorprimarynozzle.Theresultsshownin Figure6

indicatetheflowrateresponsetimeisnearlyequalto the

flowresidencetime(nogasdynamiclag).Thispredictionis

intuitivelyreasonablebecauseof thehighflowvelocities

andrelativelysmallductvolumeinvolved.

Application of CFD for Model Ref'mement

Two assumptions in the modeling technique that must

be explored further are the self-similar prof'de assumption

and the proposed function for the kinetic energy exchange

mechanism. One avenue for examining internal flow conditions is to analyse the internal flowfield with CFD.

FIDAP, a commercial CFD finite-element analysis code

(Reference 11), was chosen for this purpose. Although the

code has a time-dependent turbulent flow solution capability, the version of the code employed could not handle

compressibility effects. Also, the CPU requirements for

unsteady flow solutions limited our investigation to steady

flow analysis. These practical restrictions aside, FIDAP was

still considered acceptable for obtaining a "snapshot" of the

internal ejector flow since a few studies hinted at some

success with this approach (Sohn, 1989; Bullock and

Haroutunian, 1989).

A simple test case was of interest that would focus on

prediction of conditions in the mixing region. For this

purpose a simple 2-D turbulent mixing layer configuration

was constructed: a primary jet is discharged through a 0.4in

high slot into a 4.88in section (constant area) mixing region.

At the time of this writing, converged turbulent flow

solutions (using the k - e turbulence model and upwinding)

have only been obtained for a 0.5 ft/s primary jet velocity.

Although this low a velocity limits the direct applicability

of the results, some qualitative comments can be made.

The velocity profiles shown in Figure 7a clearly illustrate

the potential core region of the primary flow. These

transition to a fully developed appearance at the end of the

duct (for clarity, only a small region of the 5in by 14in mixing

region is shown). A test of the appropriateness of the

Abramovich self-similar profile assumption is shown in

Figure 7b. Turbulent flow profiles at the axial stations

z/d= 18 and 30, and the solution for a laminar flow at

z/d = 30 are plotted against the Abramovich profile. It is

interesting to note how closely the laminar flow solution

follows the turbulent approximation. For the turbulent flow

computation, we observe that the fully-developed profile

assumption is clearly more appropriate at z/d = 30 than at

18.

It is evident from these results that it is important to

include the potential core in the velocity profile representation. Also, some account of the developing nature of the

flow is warranted for z/d < 30.

S.umma_

An ejector simulation method that includes ejector

transients and with the potential to run real-time has been

presented. The finite volume method permits rapid evaluation of the time dependence of field variables in a thrust

augmenting ejector mixing region. For complete

verification of the proposed modeling technique it is necessary to have available transient ejector performance data

to compare with the simulation output. At the present time,

however, only steady-state tests have been conducted for

the ejector shown in Figure 1; a test plan is in-progress to

expand our database to include transient flow experimental

data.

Stability problems appear to be indicating a need for

improvements in the model for the case of choked primary

nozzle flows. Although the present model is valid for

compressible flow, entropy changes must be accounted in

a more direct way for a proper treatment of shock flow

conditions. The self-similar profiles are obviously not

appropriate in dealing with such flows.

Concern over the use of a constant value of C 1 results

in its variation with limits on the primary flow. It remains

to derive a rational form for a function (instead of a

constant) to be used for matching thust at these extremes.

Futher CFD activity is in-progress for computation of

higher-speed flows and for a geometry that is more representative of the proposed ejector configuration.

References

1. Abramovich,G. (1963), The Theory of Turbulent Jets,

MIT Press.

2. Addy,A. and Dutton,J. (1974),"Ejector-diffuser theory

and experiments," Report No.UILU-ENG-74-4009,

University of Illinois at Urbana-Champaign.

3. Akhter, M.M., Vincent, J.H. Berg, D.F., and Bodden,

D.S. (1989), "Simulation Development for US/Canada

ASTOVL Controls Technology Program," 20th Modeling and Simulation Conference, May 4-5, Pittsburg,

Pennsylvania.

4. Anderson, D., Tannehil, J., and Pletcher, R. (1984),

Computational Fluid Mechanics and Heat Transfer,

New York: McGraw Hill.

5. Bullock, C.E. and Haroutunian, V. (1989), "Analysis of

Air Circulation Patterns Within the Sistine Chapel

With a Proposed Air Conditioning System," Proceedings of the Third FIDAP Users Conference, September

24-26.

6. Choi, Y. and Soh, S. (1990), "Computational Analysis

of the Flowfieid of a Two-Dimensional Ejector

Nozzle," AIAA-90-1901.
14.

7. Chow, W.L. and Addy,A.L. (1964), "Interaction

between primary and secondary streams of supersonic

ejector systems and performance characteristics,"

AL4A Journal, V.2, No.4, pp.686-695.

8. Deese, J.E. and Agarwal, R.K. (1988), "A Numerical

Study of Viscous Flows in Inlets and Augrnentors,"

AIAA-88-O18Z

9. Donsi, G. Massimilla, L. and Colantuoni, L. (1980),

"The Dispersion of Axisymmetric Gas Jets in Fluidised

Beds," Fluidization, Grace and Matsen (Eds.) Plenum

Press: New York.

10. Drummond, C.K. (1988), "A Control-volume method

of analysis of unsteady thrust augmenting ejector

flows," NASA CR-182203.

11. FluidDynamics International (1987), FIDAP, Volumes

1-4, Evanston Illinois.

12. Goebel, S.G. and Dutton, J.C. (1990), "Velocity Measurements of Compressible, Turbulent Mixing Layers,"

AIAA-90-0709.

13. Korst,H. and Chow,W. (1966), "Non-isoenergetic turbulent jet mixing between two compressible streams at

constant pressure," NASA-CR-419.

Lowrie, B. (1990), "A Multi-Zone k-E Turbulence

Model for Complex Configurations", AIAA-90-2001.

15. McLachlan, B.G., Krothapalli, A. and Nagaraja, K.

(1984), "Flow Structure within a Heated Rectangular

Jet Ejector," A/AA Paper 84-0571.

16. Mihaloew, J.R. and Drummond, C.K. (1989), "STOVL

Aircraft Simulation for Integrated Flight and Propulsion Controls Research," NASA TM-102419.

17. Peyret, R. and Taylor,T. (1982), Computational

Methods for Fluid Flow, New York: Springer-Verlag.

18. Porter,J. and Squyers,R. (1981),"A summary/overview

of ejector augmentation theory and performance,"

USAF Technical Report No.R-91100-9CR-4Z

19. Sohn, J.L. (1989), "Numerical Analysis of Laminar and

Turbulent Incompressible Flows Using the Finite

Element 'Fluid Dynamics Analysis Package FIDAP'",

NASA CR-179390.

20. Storms, B.L. (1989), "An Experimental Study of a

Three-Dimensional Thrust Augmenting Ejector Using

Laser Doppler Velicometry," NASA CR-177531.

Tan, B.K. (1982), "Filtration of Gases in Modile

Granular Beds," Ph.D. Dissertation, University of

Cambridge (U.K.).

Thompson,P. (1972), Compressible Fluid Dynamics,

New York: McGraw-Hill.

Townsend, A.A. (1980), The Structure of Turbulent

Shear Flow, Cambridge University Press.

21.

22.

23.

z

rud _ Z

Fig. 1 Ejector configuration for STOVL aircraft
.=_

hT

o

z

I0.0

0.0

-I0.0

0.1

Natural FrequenCy

Propulsion Control System Characteristic

(Closed Loop) _ . i

....

% i

,. Ejedor lesponse

• --. \ ". ' \ (O.Loop)

%% %% f

Nominal t \ 1

.--_- l_,=.d _ \ .

I - . w | _ I !

I.o 10.0 lOO I00O

Frequency (rad/sec)

Fig. 2 Response of ejector that can be approximated by quasi-steady model

Secondary Flow

' Primar7

Potential Core

nner Boundary

-'X

t

I

Secondary

Potenlial Core

B

b

\

\'\

Outer Boundary

y layer

fix

X

I

Devdoping Developed Flow

Regime Regime

i

i

i

I

!

k-1 k k+l

SI;llion

Fig. 3 Features of the mixing region

Entrained flo_

nodes

Station i Station j

1-

_ Mixing Region Nodes

Fig. 4 Computational grid

Entrained Flow

Primary Flow

9
2

b-,

,O

-3

1211

1165

1

1075

1030

985

940

21,9 lb_

S

C 1 =

/

/

total predicted thrust

Primary nozzle flowrate

_ = 18.7 10_

S

850

0 1.5 3.0 4.5 6.0 75 9.0 10.5

TIME (milliseconds)

12.0

m

v

24.1

22.5

20.9

19.3

17.7

Fig. 5 Result from ejector transient flow test case

= _v,+(l-_)u_ _;=0.5

rit 18.7 I b '_

$

_Discharge

16.1 I I t I I 1 t r I

0 3 6 9 12 15 18 21 24 27

Fig. 6

Time (ms)

Result from duct transient flow test case

ORIGINAL PAGE IS

OF POOR QUALITY

30

10

=
Primary Flow

FIDAP Turbulent Flow Solution:

0.5 ft/s primary velocity l

a) Mixing region velocity predictions

?

"8

>,

o

¢)

;>

.o

¢)

E

"t3

O

Z

100

0.90

0.80

0.70

0.60

0.50

0.40

0.30

0.20

0.10

0.00

0.00

IDAP Laminar Flow, z/d = 30

_ramovich Theory

......__. FIDAP Turbulent Flow, z/d = 30

FIDAP Turbulent FIo_vi

z/d =

t I I 1 I I I I

0.10 0.20 0.50 0.40 0.50 0.60 0.70 0,80 0.90 1.00

Nondimensional Transverse Position, x/b

b) Self-similar velocity profiles

Fig. 7 CFD velocity predictions

11
Nalionat Aeronautics and Report Documentation Page

Space Administralion

1. Repod No.

NASA TM-103167

AIAA-90-2417

4, Title and Subtitle

....

2. Government Accession No.

A Modeling Technique for STOVL Ejector and Volume Dynamics

7. Author(s)

C.K. Drummond and W.S. Barankiewicz

9 Performing Organization Name and Address

National Aeronautics and Space Administr_tion

Lewis Research Center

Cleveland, Ohio 44135-3191

12 Sponsoring Agency Name and Address

National Aeronautics and Space Administration

Washington, I).C. 20546-0001

15. Supplementary Notes

3, Recipient's Catalog No.

5. Report Date

6, Performing Organization Code

8. Performing Organization Report No.

E-5539

10, Work Unit No.

505-62-71

11. Contract or Grant No.

13. Type of Report and Period Covered

Technical Memorandum

14, Sponsoring Agency Code

i

J

Prepared h)r the 26th Joint Propulsion Conference cosponsored by the AIAA, SAE, ASME, and ASEE, Orlando,

Florida, July 16-18, 1990.

16. Abstract

New models fi_r thrust au_ncntin_ ejector peribrmance prediction and feeder duct dynamic analysis are presented

and applied to a proposc_TOVL-_aircraft configuration. Central to the analysis is the nontraditional treatment of

the time-dependent volumc'intcgra'[s in the otherwise conventional control-volume approach. In the case of the

thrust augmenting ejector, the analysis required a new relationship for transfer of kinetic energy from the primary

flow to the secondary flow. Extraction of the required empirical corrections from current steady-state

cxperirncntal_d,'ita is discussed; a poss!ble approach for modelling insight through CFD-is presented.

f

J

l

=

S

l

s

17. Key Words (Suggested by Author(s))

STOVL propulsion

Ejector augmenter

Transient flow

18. Distribution Statement

Unclassified - Unlimited

Subject Category 07

19. Security Classif. (of this report) _[ 20. Security Ctas_ff. (of this page) [ 21. No. of pages

Unclassified Unclassified 12

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